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On a representation of the idele class group related to primes and zeros of L-functions
Ralf Meyer
Source: Duke Math. J. Volume 127, Number 3
(2005), 519-595.
Abstract
Let K be a global field. Using natural spaces of functions on the adele ring and the idele class group of K, we construct a virtual representation of the idele class group of K whose character is equal to a variant of the Weil distribution which occurs in André Weil's explicit formula. Hence this representation encodes information about the distribution of the prime ideals of K and is a spectral interpretation for the poles and zeros of the L-function of K. Our construction is motivated by a similar spectral interpretation by Alain Connes.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1113847338
Digital Object Identifier: doi:10.1215/S0012-7094-04-12734-4
Mathematical Reviews number (MathSciNet): MR2132868
Zentralblatt MATH identifier: 02177466
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